Harmonics

Let's illustrate this concept by considering a flute or non-electronic organ; one of the most simple natural oscillation sources - the sound produced is not much more than a sinewave whistle sound. Generally, the pitch that you'll hear when you listen to the sound of the instrument is the first harmonic (the fundamental) - the basic frequency that the air vibrates at dictated by the pipe length. But, a flute or organ sounds richer than just a pure sinewave. Why? Because of harmonics - extra overtones at frequencies above the fundamental. the second harmonic is half the wavelength of the fundamental and therefore twice the frequency. In isolation we would perceive this as a tone exactly one octave above the fundamental. The third harmonic has a frequency of three times that of the fundamental (one and a half octaves above the fundamental) and the fourth harmonic, with a frequency of four times that of the fundamental, defines the second octave above the fundamental. And so it goes on...

In other words, the harmonic structures of oscillating items are closely related to one another, and we hear this as musically 'pleasing'.

Simple Harmonic Series
How does this relate to forms of synthesis? read on...